Susan A. Frost

Load Balancing in Control Allocation

Next-generation aircraft with a large number of actuators will require advanced control allocation methods to compute the actuator commands needed to follow desired trajectories while respecting system constraints. Previously, algorithms were proposed to minimize the l 1 or l 2 norms of the tracking error and of the actuator deflections. This paper discusses the alternative choice of the l ∞ norm, or the sup norm. Minimization of the control effort translates into the minimization of the maximum actuator deflection (min―max optimization). This paper shows how the problem can be solved effectively by converting it into a linear program and solving it using a simplex algorithm. Properties of the algorithm are also investigated through examples. In particular, the min―max criterion results in a type of load balancing, where the load is the desired command and the algorithm balances this load among various actuators. The solution using the l ∞ norm also results in better robustness to failures and lower sensitivity to nonlinearities in illustrative examples. This paper also discusses the extension of the results to a normalized l ∞ norm, where the norm of the actuator deflections are scaled by the actuator limits. Minimization of the control effort then translates into the minimization of the maximum actuator deflection as a percentage of its range of motion.

Adaptive Disturbance Tracking Control for Large Horizontal Axis Wind Turbines in Variable Speed Transition Operation

Renewable energy is becoming more important all over the world, and wind energy is the most important role in renewable energy right now. Many countries are producing and building wind turbines, and the turbine size is becoming larger. The larger a turbine is, the more expensive it will be. However, wind turbines will fail when overspeeding. So we need control algorithms to protect the turbine and to develop power output efficiency. The study concerns the implementation of adaptive control on a Horizontal Axis Wind Turbine (HAWT). This paper focuses on the implementation of adaptive control in the Transition Region between Region 2 and Region 3. For Region 2, Adaptive Disturbance Tracking Control (DTC) with a certain tracking ratio will ensure the wind turbine has maximum power capture. Using the same Adaptive DTC in the Transition Region, but with a switching mechanism for different tracking ratios, the wind turbine will have smooth performance for connecting Region 2 and Region 3.

Robust adaptive model tracking for distributed parameter control of linear infinite-dimensional systems in Hilbert space

This paper is focused on adaptively controlling a linear infinite-dimensional system to track a finite-dimensional reference model. Given a linear continuous-time infinite-dimensional plant on a Hilbert space with disturbances of known waveform but unknown amplitude and phase, we show that there exists a stabilizing direct model reference adaptive control law with the properties of certain disturbance rejection and robustness. The plant is described by a closed, densely defined linear operator that generates a continuous semigroup of bounded operators on the Hilbert space of states. The central result will show that all errors will converge to a prescribed neighborhood of zero in an infinite-dimensional Hilbert space. The result will not require the use of the standard Barbalats lemma which requires certain signals to be uniformly continuous. This result is used to determine conditions under which a linear infinite-dimensional system can be directly adaptively controlled to follow a reference model. In particular, we examine conditions for a set of ideal trajectories to exist for the tracking problem. Our results are applied to adaptive control of general linear diffusion systems described by self-adjoint operators with compact resolvent.

CONTROL ALLOCATION WITH LOAD BALANCING

Next generation aircraft with a large number of actuators will require advanced control allocation methods to compute the actuator commands needed to follow desired trajectories while respecting system constraints. Previously, algorithms were proposed to minimize the l1 or l2 norms of the tracking error and of the actuator deflections. The paper discusses the alternative choice of the l∞ ∞ ∞ ∞ norm, or sup norm. Minimization of the control effort translates into the minimization of the maximum actuator deflection (min-max optimization). The paper shows how the problem can be solved effectively by converting it into a linear program and solving it using a simplex algorithm. Properties of the algorithm are also investigated through examples. In particular, the min-max criterion results in a type of load balancing, where the load is the desired command and the algorithm balances this load among various actuators. The solution using the l∞ ∞ ∞ ∞ norm also results in better robustness to failures and to lower sensitivity to nonlinearities in illustrative examples.

Distributed Parameter Direct Adaptive Control Using a New Version of the Barbalat-Lyapunov Stability Result in Hilbert Space

Abstract: Given a linear continuous-time infinite-dimensional plant on a Hilbert space and disturbances of known waveform but unknown amplitude and phase, we show that there exists a stabilizing direct model reference adaptive control law with certain disturbance rejection and robustness properties. The plant is described by a closed, densely defined linear operator that generates a continuous semigroup of bounded operators on the Hilbert space of states. The central result is an extension of Barbalat-Lyapunov result for infinite dimensional Hilbert spaces. This is used to determine conditions under which a linear Infinite-dimensional system can be directly adaptively regulated. Our results are applied to adaptive control of general linear diffusion systems.

Resource balancing control allocation

Next generation aircraft with a large number of actuators will require advanced control allocation methods to compute the actuator commands needed to follow desired trajectories while respecting system constraints. Previously, algorithms were proposed to minimize the l1 or l2 norms of the tracking error and of the control effort. The paper discusses the alternative choice of using the l1 norm for minimization of the tracking error and a normalized l221E; norm, or sup norm, for minimization of the control effort. The algorithm computes the norm of the actuator deflections scaled by the actuator limits. Minimization of the control effort then translates into the minimization of the maximum actuator deflection as a percentage of its range of motion. The paper shows how the problem can be solved effectively by converting it into a linear program and solving it using a simplex algorithm. Properties of the algorithm are investigated through examples. In particular, the min-max criterion results in a type of resource balancing, where the resources are the control surfaces and the algorithm balances these resources to achieve the desired command. A study of the sensitivity of the algorithms to the data is presented, which shows that the normalized l221E; algorithm has the lowest sensitivity, although high sensitivities are observed whenever the limits of performance are reached.

Adaptive Disturbance Tracking theory with state estimation and state feedback for region II control of large wind turbines

A theory called Adaptive Disturbance Tracking Control (ADTC) is introduced and used to track the Tip Speed Ratio (TSR) of 5 MW Horizontal Axis Wind Turbine (HAWT). Since ADTC theory requires wind speed information, a wind disturbance generator model is combined with lower order plant model to estimate the wind speed as well as partial states of the wind turbine. In this paper, we present a proof of stability and convergence of ADTC theory with lower order estimator and show that the state feedback can be adaptive.

Coupled Aeroelastic Vortex Lattice Modeling of Flexible Aircraft

This paper presents a recently developed computational tool for aeroelastic analysis of aircraft performance. The computational tool couples a vortex-lattice code, Vorview, with an aeroelastic model that computes wing structural deflections under a combined coupled bending-torsion motion. The aeroelastic model of the wing structure is based on a one-dimensional structural dynamic theory using steady state aerodynamics assumption. An automated aircraft geometry modeler is developed to generate a deformed aircraft geometry based on the structural deflection aeroelastic analysis. The computation is iterated until the solution converges within a specified error tolerance. This computational tool is capable to predict both steady state aerodynamics as well as aeroelastically induced unsteady aerodynamics. Simulations are conducted for a generic transport aircraft to demonstrate the capability of the computational tool.

Evolving Systems: Adaptive Key Component Control and Inheritance of Passivity and Dissipativity

We propose a new framework called Evolving Systems to describe the self-assembly, or autonomous assembly, of actively controlled dynamical subsystems into an Evolved System with a higher purpose. Autonomous assembly of large, complex flexible structures in space is a target application for Evolving Systems. A critical requirement for autonomous assembling structures is that they remain stable during and after assembly. The fundamental topic of inheritance of stability, dissipativity, and passivity in Evolving Systems is the primary focus of this research. In this paper, we develop an adaptive key component controller to restore stability in Nonlinear Evolving Systems that would otherwise fail to inherit the stability traits of their components. We provide sufficient conditions for the use of this novel control method and demonstrate its use on an illustrative example.

Modified Adaptive Control for Region 3 Operation in the Presence of Wind Turbine Structural Modes

‡Many challenges exist for the operation of wind turbines in an efficient manner that is reliable and avoids component fatigue and failure. Turbines operate in highly turbulent environments resulting in aerodynamic loads that can easily excite turbine structural modes, possibly causing component fatigue and failure. Wind turbine manufacturers are highly motivated to reduce component fatigue and failure that can lead to loss of revenue due to turbine down time and maintenance costs. The trend in wind turbine design is toward larger, more flexible turbines that are ideally suited to adaptive control methods due to the complexity and expense required to create accurate models of their dynamic characteristics. In this paper, we design an adaptive collective pitch controller for a high-fidelity simulation of a utility-scale, variable-speed horizontal axis wind turbine operating in Region 3. The objective of the adaptive pitch controller is to regulate generator speed, accommodate wind gusts, and reduce the excitation of structural modes in the wind turbine. The control objective is accomplished by collectively pitching the turbine blades. The adaptive collective pitch controller for Region 3 was compared in simulations with a baseline classical Proportional Integrator (PI) collective pitch controller. The adaptive controller will demonstrate the ability to regulate generator speed in Region 3, while accommodating gusts, and reducing the excitation of certain structural modes in the wind turbine.